Conditional Statements

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What is a conditional statement?

Back

A conditional statement is an if-then statement that expresses a relationship between two propositions, where one proposition (the hypothesis) implies the other (the conclusion).

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What is the hypothesis in a conditional statement?

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The hypothesis is the part of a conditional statement that follows 'if'. It represents the condition that must be met for the conclusion to be true.

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What is the conclusion in a conditional statement?

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The conclusion is the part of a conditional statement that follows 'then'. It represents the result or outcome that follows from the hypothesis.

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What does it mean to negate a statement?

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To negate a statement means to state the opposite of that statement. For example, the negation of 'It is raining' is 'It is not raining'.

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What is the inverse of a conditional statement?

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The inverse of a conditional statement 'If P, then Q' is 'If not P, then not Q'.

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What is the converse of a conditional statement?

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The converse of a conditional statement 'If P, then Q' is 'If Q, then P'.

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What is the contrapositive of a conditional statement?

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The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P'.

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How do you write the negation of 'If I win, then you don't lose'?

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The negation is 'I win and you lose'.

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What is the relationship between a statement and its contrapositive?

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A conditional statement and its contrapositive are logically equivalent; if one is true, the other is also true.

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What is the relationship between a statement and its inverse?

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A conditional statement and its inverse are not logically equivalent; one can be true while the other is false.